A statistical model is a set of mathematical equations which describe the behavior of an object of study in terms of random variables and their associated probability distributions. For example, in order to forecast and manage business risk, a set of variables are identified that describe the state of the world and are forecasted into the future. These variables are often termed risk factors. Each risk factor has different attributes and behaviors and is a unique contributor to the entire system.
Risk management refers to the design and implementation of procedures for identifying, measuring, and managing risks. A risk manager desires to be prepared for possible deleterious movements of the risk factors. To determine possible future values, a forecast is performed. The forecast of interest may not be a single point but a distribution of possible values in the future. The distribution of risk factors may be modeled using various approaches such as: Monte Carlo simulation, historical simulation, scenario simulation, etc.